Free Printable MIDTERM EXAMINATION

1.

$27x^2\div9x$ (AVOID SPACING)

(a)

2.

$14m^2n^2\div7mn$ (AVOID SPACING)

(a)

3.

Divide:

a)

$2x^8-8x^2-28x$

b)

$2x^8-2x^2-7x$

c)

$8x^7-8x-28x$

d)

$2x^7-2x-7$

4.

Divide:

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

5.

a)

-5x¹⁰

b)

4x⁴+ 18x⁶

c)

-6x⁴+ 16x²

d)

4x⁴- 9x²

6.

a)

5w² − 4w + 3

b)

12w² − 9w + 6

c)

12w² − 12w + 9

d)

5w² − 12w+ 9

7.

Divide:

(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

8.

$Divide\ 8x^2-4x\ +12\ by\ 2x$

a)

$4x+2$

b)

$\frac{4x-2+6}{x}$

c)

$4x-2$

d)

$\frac{4x-2+1}{6x}$

9.

Divide 16x⁴ + 8x³ - 4x² by 4x²

a)

12x² + 4x

b)

12x² + 4x - 1

c)

4x² + 2x - 1

d)

4x² + 2x

10.

$\frac{\text{3}x^2-2xy}{\text{2x}}$

a)

$1.5x^{3\ }-x^2y$

b)

$1.5x\ -\ y$

c)

$1.5x\ +\ y$

d)

$1.5x\ -\ 2y$

11.

$\frac{6a^3b^2c^{4\ }-\ 8a^2b^2c}{2a^2bc}$

a)

$3abc\ -\ 4abc$

b)

$3abc^{3\ }-\ 4b$

c)

$3a^3b^2c^{4\ }-\ 4b$

d)

$3abc\ +4b$

12.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

13.

Evaluate the expression using the quotient rule.

a)

x¹³

b)

x⁵

c)

x³⁶

d)

x^-5

14.

25x⁵/5x³

a)

5x

b)

5x⁸

c)

-5x²

d)

5x²

15.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

16.

3.) Simplify
(45x⁶y⁹) / (5x⁴y²)

a)

(9x²)/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

17.

Simplify.

a)

6r⁶

b)

3r⁴

c)

3r⁶

d)

6r⁴

18.

Simplify this expression.

a)

-5x¹⁰

b)

4x⁴+ 18x⁶

c)

-6x⁴+ 16x²

d)

4x⁴- 9x²

19.

Divide (6x²+12x) by 3x

a)

2x+4

b)

2+6/3x

c)

2+4/x

d)

3+6/2x

20.

Simplify this expression.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

21.

Simplify this expression.

a)

-5x¹⁰

b)

4x⁴+ 18x⁶

c)

-6x⁴+ 16x²

d)

4x⁴- 9x²

22.

Divide (6x²+12x) by 3x

a)

2x+4

b)

2+6/3x

c)

2+4/x

d)

3+6/2x

23.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

24.

a)

1/m²

b)

m²

c)

m⁸

d)

1/m⁸

25.

a)

5w² − 4w + 3

b)

12w² − 9w + 6

c)

12w² − 12w + 9

d)

5w² − 12w+ 9

26.

When I am a dividing by a monomial, I should _______ the coefficients and ________ the exponents for each term.

a)

add, subtract

b)

subtract , divide

c)

divide, divide

d)

divide, subtract

27.

$\frac{20x^2}{5x}$

a)

$15x$

b)

$4x$

c)

$15x^2$

d)

$25x$

28.

$\frac{36m^2n^5}{9m^2n^3}$

a)

$27n^2$

b)

$4mn^2$

c)

$45m^4n^8$

d)

$4n^2$

29.

$\frac{\left(5x^2-15y^3\right)}{5}$

a)

$x^2-3y^3$

b)

$x^2-15y^3$

c)

$10x^2-20y^3$

d)

$5x^2-3y^3$

30.

$\frac{\left(m^2n+m^6n^3\right)}{mn}$

a)

$m^3n^2+m^7n^4$

b)

$m^2n+m^5n^2$

c)

$m+m^5n^2$

d)

$m+m^6n^3$

31.

What is $6b^3+12b^4c^2$ divided by $3b^2$

a)

$2b+4b^2c^2$

b)

$3b+9b^2c^2$

32.

$\left(14d^3-21d^8\right)\div\ 7d^2$

a)

$7d-21d^6$

b)

$7d^{1.5}-14d^4$

c)

$2d-3d^6$

d)

$2d^{1.5}-3d^4$

33.

$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$

a)

$-15x^4-9x^2-3x$

b)

$-6x^4-4x^2-2x$

c)

$6x^4+4x^2+2x$

d)

$6x^5+4x^3+2x^2$

34.

$\frac{\left(x^6y^8-x^4y^6+x^2y^4\right)}{x^2y^2}$

a)

$x^4y^6-x^2y^4+y^2$

b)

$x^3y^4-x^2y^3+xy^2$

c)

$x^8y^{10}-x^6y^8+x^4y^6$

d)

$0x^4y^6-0x^2y^4+0y^2$

35.

Divide 8x² -4x + 12 by 2x

a)

4x+2

b)

4x-2+6/x

c)

4x-2

d)

4x-2+1/(6x)

36.

Divide 16x⁴ + 8x³ - 4x² by 4x²

a)

12x² + 4x

b)

12x² + 4x - 1

c)

4x² + 2x - 1

d)

4x² + 2x

37.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

38.

Simplify
$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

$\frac{5x^6}{2}$

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

39.

$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$

a)

$4x^2+3x-5$

b)

$4x^2+3x^{1.5}-5x$

c)

$6x^2+4x-12$

d)

$6x^2+4x^{1.5}-12x$

40.

What is the GCF of 4 and 12?

a)

3

b)

1

c)

6

d)

4

41.

What is the GCF of 18 and 24?

a)

3

b)

6

c)

8

d)

9

42.

Find the GCF of 64 and 144

a)

8

b)

6

c)

16

d)

2

43.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

44.

What is the GCF? 3x²-2x

a)

3

b)

3x

c)

x

d)

2

45.

What is the GCF of 18k and 15k³

a)

3k²

b)

3k³

c)

3k

d)

5k

46.

What is the GCF? 2x²-4x+8

a)

2x

b)

2

c)

x

d)

1

47.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

48.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

49.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

50.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

51.

Factor:
2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

52.

Factor out the GCF

3x³ + 9x

a)

3x (x²+ 3)

b)

3x ( x³ + 9)

c)

x (3x² + 9)

d)

3x (x³ + 3x)

53.

Factor completely

18x³ + 81x - 27

a)

9x (2x² + 9x - 3)

b)

3 (6x³ + 27x - 9)

c)

9 (2x³ + 9x - 3)

d)

9 (2x² + 9x - 3)

54.

Factor:
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

55.

Factor
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

56.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

57.

Factor by GCF:

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

Prime

58.

Factor by GCF:

17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

Prime

59.

What is the GCF of 18k and 15k³

a)

5k³

b)

3k³

c)

3k

d)

5k

60.

What is the greatest common factor of the three terms in the expression?
24m³n⁵p + 6mn⁴p² + 4mn⁵

a)

2mn

b)

24mn⁴

c)

2mn⁴

d)

2mn⁴p

61.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

62.

Factor using the GCF method
8r³ + 16r²

a)

4r²(2r + 4)

b)

8r²(r + 2)

c)

8(r³ + r²)

d)

4(r³ + 2r²)

63.

Which is a factor of $x^2-11x+24?$

a)

$\left(x+3\right)$

b)

$\left(x-3\right)$

c)

$\left(x+4\right)$

d)

$\left(x-4\right)$

64.

Which of the following is one of the factors of the expression: $4x^2-25?$

a)

$\left(4x-5_{ }\right)$

b)

$\left(2x+1\right)$

c)

$\left(4x-1\right)$

d)

$\left(2x-5\right)$

65.

What is the factored form of the expression? $x^2-16$

a)

$\left(x-4\right)\left(x+4\right)$

b)

$\left(x-8\right)\left(x+8\right)$

c)

$\left(x-4\right)\left(x-4\right)$

d)

$\left(x-8\right)\left(x-8\right)$

66.

Which shows the polynomial $8x^2+16x+8$ completely factored?

a)

$\left(4x+4\right)^2$

b)

$\left(4x+4\right)\left(2x+2\right)$

c)

$8\left(x+1\right)^2$

d)

$8\left(x+1\right)\left(x-1\right)$

67.

What is the factored form of the expression? $x^2+x-6$

a)

$\left(x-3\right)\left(x+2\right)$

b)

$\left(x+1\right)\left(x-6\right)$

c)

$\left(x-2\right)\left(x+3\right)$

d)

$\left(x-2\right)\left(x-3\right)$

68.

What are the binomial factors of $x^2+7x-18$

(Pick 2 answers)

a)

$\left(x-9\right)$

b)

$\left(x+9\right)$

c)

$\left(x-2\right)$

d)

$\left(x+2\right)$

69.

If $\left(x-3\right)$ is a factor of $x^2+x-12$ , then the other factor is?

a)

$\left(4x-3\right)$

b)

$\left(3x-4\right)$

c)

$\left(x-4\right)$

d)

$\left(x+4\right)$

70.

Written in factored form, the trinomial $2y^2+26y+80$ is equivalent to:

a)

$2\left(y-5\right)\left(y-8\right)$

b)

$\left(2y+5\right)\left(y+8\right)$

c)

$2\left(y+5\right)\left(y+8\right)$

d)

$\left(y+5\right)\left(2y+16\right)$

71.

When factored completely, $x^3-9x$ is equivalent to:

a)

$x\left(x-3\right)$

b)

$x\left(x+3\right)\left(x-3\right)$

c)

$\left(x+3\right)\left(x-3\right)$

d)

$x\left(x+3\right)$

72.

Which expression is the factored form of $2x^2-2x-12?$

a)

$2\left(x+2\right)\left(x-3\right)$

b)

$2\left(x+6\right)\left(x-1\right)$

c)

$2\left(x+3\right)\left(x-2\right)$

d)

$2\left(x+1\right)\left(x-6\right)$

73.

If $\left(x-3\right)$ and $\left(x+7\right)$ are the factors of the trinomial $x^2+bx-21$ , what is the value of b?

a)

$-3$

b)

$-4$

c)

$7$

d)

$4$

74.

If $\left(2x-3\right)$ and $\left(x+5\right)$ are multiplied to form the trinomial $ax^2+bx+c$ , what is the value of b?

a)

$-15$

b)

$2$

c)

$7$

d)

$4$

75.

Factor the trinomial completely. $x^2-x-30$

a)

$\left(x+1\right)\left(x-30\right)$

b)

$\left(x+5\right)\left(x-6\right)$

c)

$\left(x+6\right)\left(x-5\right)$

d)

$prime$

76.

Factor the trinomial completely. $x^2-6x-72$

a)

$\left(x-12\right)\left(x+6\right)$

b)

$\left(x-72\right)\left(x+1\right)$

c)

$\left(x+12\right)\left(x-6\right)$

d)

$prime$

77.

Factor the binomial completely. $36-25x^2$

a)

$\left(6-5x\right)^2$

b)

$\left(6+5x\right)^2$

c)

$\left(6+5x\right)\left(6-5x\right)$

d)

$prime$

78.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

79.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

80.

w⁴ - 625

a)

(w² + 25) (w² - 25)

b)

(w² - 25) (w² - 25)

c)

(w²+ 25) (w+5) (w-5)

d)

(w+25)(w-25)

81.

x⁶- 400

a)

( x³ - 200) ( x³ + 200)

b)

( x² + 20) ( x² + 20)

c)

( x - 20) ( x + 20)

d)

( x³ - 20) ( x³ + 20)

82.

x⁴ - 100y²

a)

(x² + 10y) (x² - 10y)

b)

(x + 10y) (x - 10y)

c)

(x + 10y) (x³ - 10y)

d)

(x³ + 10y) (x - 10y)

83.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

84.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

85.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

86.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

87.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

88.

Factor the GCF
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

89.

Factor the GCF
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

90.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

91.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

92.

Factor
5x²-28x+32

a)

(3x-10)(x+6)

b)

(x-8)(5x-4)

c)

(5x-8)(x-4)

d)

(5x-8)(x+7)

93.

Factor
4x²-25x+25

a)

4(x-5)(x+5)

b)

(x+5)(4x+5)

c)

(x-5)(4x-5)

d)

(x+2)(9x+1)

94.

Factor the GCF
63x⁴ - 7x² + 28x

a)

7x(9x² - 7 + 4x)

b)

x(63x³ - 7x + 28)

c)

7x(9x³ - x + 4)

d)

not factorable

95.

Factor the GCF
39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

d)

not factorable

96.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

97.

Factor Completely: 5x²-11x+6

a)

(5x+6)(x-1)

b)

(5x-6)(x-1)

c)

(2x-7)(x-3)

d)

(5x-6)(x+1)

98.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

99.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

100.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

MIDTERM EXAMINATION

Total questions: 100

Worksheet time: 25hrs 0mins

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